Question

Find f(5) for this sequence:
f(1) = 2 and f(2) = 4, f(n) = f(1) + f(2) + f(n - 1), for n > 2.

f(5) = ______

Answer 1

ok so what is the first two terms of the sum?

? + ? + ?

Answer 2

i have no idea

Answer 3

the first two terms are f(1) + f(2) so what are they?

Answer 4

ok heres a hint because there is a lot more to the problem

Answer 5

the first two terms are 2 + 4

Answer 6

they are given to you

Answer 7

now the third term is tricky, f(n-1) , that is recursive, so it will create several terms in the final sum

Answer 8

are you with me so far, we have 2 + 4 + f(n-1)

Answer 9

yes i am (:

Answer 10

ok so now lets ignore the 2+4 for a minute and focus on f(n-1)

Answer 11

so what is n?

Answer 12

2 + 4 + f(n-1) = f(n)=-6?

Answer 13

no, what is n?

Answer 14

f(n), we have f(5) so what is n?

Answer 15

just match the pattern you see given f(n) and f(5)

Answer 16

the f is the same but the other part is different

Answer 17

ok another hint, n = 5

Answer 18

ok so f(5) = f(1) + f(2) + f(n - 1)

we already know f(1) and f(2)

so we can write as

2 + 4 + f(n - 1)

but we also know n so we can write as

2 + 4 + f(5 -1)

if we subtract one from the 5 we have

f(5) = 2 + 4 + f(4)

Answer 19

now you need to find f(4), which starts 1 + 2 +...

Answer 20

Directly substitute n = 5 into the formula.

f(5) = f(1) + f(2) + f(4) .. We know f(1) = 2, and f(2) = 4 so

f(5) = 2 + 4 + f(4) = 6 + f(4). Now determine f(4) . . .

f(4) = f(1) + f(2) + f(3) = 6 + f(3)... so..

f(5) = 6 + (6 + f(3) ) = 12 + f(3)
right?

Answer 21

you got the idea, yep

Answer 22

so it will be some positive number

Answer 23

f(5) = 6+16
f(5) = 22

Answer 24

?

Answer 25

sounds good to me

Answer 26

thanks you so much could you help me with one more?

Answer 27

sure, by the way u see that pattern was 6*(n-2) + f(2) or 6*(n-2) + 4 is the general solution for any n

Answer 28

yes i did (:

Answer 29

ok perfect, u understand this very well

Answer 30

Generate the first 5 terms of this sequence:
f(1) = 2 and f(2) = 3, f(n) = f(n - 1) + f(n - 2), for n > 2


A.) 2, 3, 5, 7, 9
B.) 2, 3, 4, 7, 11
C.) 2, 3, 5, 9, 11
D.) 2, 3, 5, 8, 13

Answer 31

ok so yeah slightly more complex but exact same idea, i recommend starting brute force like we did before until you see a general pattern, unless you can just see the pattern right away

Answer 32

you already know the first two terms which is nice, so you just need f(3), f(4), and f(5)

Answer 33

so just plug and chug

Answer 34

C?

Answer 35

no i dont think so

Answer 36

so whats f(3)

Answer 37

aka the third term

Answer 38

ohhh i new at is D 2, 3, 5, 8, 13

Answer 39

yeah i beleive thats correct

Answer 40

thanks again for you time & help!!!(:

Answer 41

yw :)